The direct reach of muon colliders vastly and generically exceeds the sensitivity of the High-Luminosity LHC (HL-LHC). This is illustrated by the solid bars on the right panel of Figure REF , where we report the projected HL-LHC mass reach [1]} on several BSM states. The \(95\%\)  CL exclusion is reported, instead of the discovery, as a quantification of the physics reach. Specifically, we consider Composite Higgs fermionic top-partners \(T\)  (e.g., the \(X_{5/3}\)  and the \(T_{2/3}\) ) and supersymmetric particles such as stops \({\widetilde{t}}\), charginos \({\widetilde{\chi }}_1^\pm \), stau leptons \({\widetilde{\tau }}\) and squarks \({\widetilde{q}}\). For each particle we report the highest possible mass reach, as obtained in the configuration for the BSM particle couplings and decay chains that maximizes the hadron colliders sensitivity. The reach of a 100 TeV proton-proton collider (FCC-hh) is shown as shaded bars on the same plot. The muon collider reach, displayed as horizontal lines for \(E_{\rm {cm}}=10\) , 14 and 30 TeV, exceeds the one of the FCC-hh for several BSM candidates and in particular, as expected, for purely electroweak charged states.
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